I have a thin red vertical line down the side of my iMac display-anybody know what this means?

Yes, the graphics card appears to be failing. If the machine was covered by AppleCare go to your Apple Store IMMEDIATELY and they may repair it considering it's only 1 month out of AppleCare coverage. If it's not covered by AppleCare then still take it into an Apple Store or AASP and look into getting it fixed.

One test you can run in Apple Hardware Test in Extended Mode, if it picks up the graphics card issue (or any other hardware problems) then you can take that error code with you when you take it in for service. Here are instructions to AHT.

http://support.apple.com/kb/HT1509

It could also be the LCD panel that is failing.

One fairly easy way to validate if it really is the graphic card that is failing, is to connect your iMac to an external screen. If the problem is not visible on your external screen, then the card is fine.

Depending on your iMac model, You need a Mini display port or a Mini dvi port to DVI, HDMI or VGA adaptor depending on the connection available on the external screen, and a cable.

If you have an HDTV, get a Mini DVI to HDMI adapter plus a HDMI cable and connect the mac to the HDMI input on your TV.

If it is the LCD that is the problem, you could decide to buy an external screen for a fraction of the cost of getting the graphic card replaced or the LCD replaced.

I am actually using a 2008 iMac with a defective LCD panel as a media server connected to my HDTV, and the image is perfect!

The computer workks perfectly well but the LCD had what seems to be the same problem as yours, but with a multitude of lines on the screen.